Points: 0.5 of 1
Use long division to find the quotient $Q (x)$ and the remainder $R (x)$ when $P (x)$ is divided by $d (x)$ and express $P (x)$ in the form $d (x) \cdot Q (x) + R (x)$ .
$\begin{array}{l} P (x) = x^{3} + 2 x^{2} - 9 x + 183 \\ d (x) = x + 7 \end{array}$
$P (x) = (x + 7)$

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Answer

$Q (x) = x^{2} - 5 x + 36, R (x) = - 69$

Steps

Step 1 ：We are given a polynomial $P (x) = x^{3} + 2 x^{2} - 9 x + 183$ and a divisor $d (x) = x + 7$ . We are asked to perform polynomial long division to find the quotient $Q (x)$ and the remainder $R (x)$ such that $P (x) = d (x) \cdot Q (x) + R (x)$ .

Step 2 ：Performing the polynomial long division, we find that the quotient is $Q (x) = x^{2} - 5 x + 36$ and the remainder is $R (x) = - 69$ .

Step 3 ：Therefore, the polynomial $P (x)$ can be expressed as $P (x) = d (x) \cdot Q (x) + R (x)$ , where $Q (x) = x^{2} - 5 x + 36$ and $R (x) = - 69$ .

Step 4 ： $Q (x) = x^{2} - 5 x + 36, R (x) = - 69$

Points: 0.5 of 1Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x) and express P(x) in the form d(x)⋅Q(x)+R(x).P(x)=x3+2x2−9x+183d(x)=x+7P(x)=(x+7)

Answer

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Points: 0.5 of 1
Use long division to find the quotient $Q (x)$ and the remainder $R (x)$ when $P (x)$ is divided by $d (x)$ and express $P (x)$ in the form $d (x) \cdot Q (x) + R (x)$ .
$\begin{array}{l} P (x) = x^{3} + 2 x^{2} - 9 x + 183 \\ d (x) = x + 7 \end{array}$
$P (x) = (x + 7)$